Constraint Theory

by Friedman, George

• ISBN13: 9781441936264
• ISBN10: 1441936262
• Format: Paperback
• Copyright: 2005-05-30
• Publisher: Springer Verlag

Summary

The enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable.This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint", literally trillions of times faster than a random search, determining consistency and compatibility within seconds.This text is an invaluable reference to all engineers, mathematicians and managers concerned with modeling.

Table of Contents

Motivations	p. 1
What Is Constraint Theory And Why Is It Important?
Trends and Problems in System Technologies
An Example of Low Dimension
The Manager and Analyst Continue their Dialogue
Preliminary Conclusions
A Little Window into Future Chapters
Problems for the Curious Reader
The Four-Fold Way	p. 25
How to Perceive Complex Mathematical Models and Well-Posed Problems
Prologue: The Manager and Analyst Discuss the Origins of Multidimensional Models and Well-Posedness
The First View: Set Theoretic
The Second View: Family of Submodels
The Third View: The Bipartite Graph
The Fourth View: The Constraint Matrix
Model Consistency and Computational Allow Ability
The Manager and Analyst Continue their Dialogue
Chapter Summary
Problems for the Interested Student
General Results	p. 49
From Protomath to Math to Metamath
Language and Mathematics
Most General Trustworthy Results
Classes of Relations
Manager and Analyst Revisited
Chapter Summary
Problems for the General Student
Regular Relations	p. 61
Searching for the Kernels of Constraint
Cognitive Barriers to Circuits
Node, Knot and Basic Nodal Square Sanctification
Useful Properties of Bapartite Graphs
Cornering the Culprit Kernels; Ten Easy Pieces
Continuing the Pursuit Inside the Circuit Clusters (CC)
Locating the BNSs in Minutes, Not University Lifetimes
Comparison of Computational Complexity; Trillions and Trillions of Times Faster
Zero Constraint All Along the Computational Path
Recapitulation of Computational Flow
General Procedure for Determining Consistency and Allow Ability in a Model of Regular Relations
Summary of Chapter and Constraint Theory Toolkit
Queries for the Regular Student
Discrete and Interval Relations	p. 111
The Diminished Utility of Metamodels
Metamodel Issues and Perspectives
The General Taxonomy and Primary Property of Discrete Relations
Bolean Relations
Topological Implications
Allowability of Discrete Computations
Inequality Relations
Summary
Problems for the Discrete Student
The Logical Structure of Constraint Theory	p. 129
A Compact Summary
Overview
Postulates and Philosophical Assumptions
Definitions
Theorems
Graphs of the Logical Structure of Constraint Theory
Completeness
Examples of Constraint Theory Applied to Real-World Problems	p. 137
Apologies Not Required
Cost as an Independent Variable (CAIV)
The Kinematics of Free-Fall Weapons
The Deflection of an Earth-Threatening Asteroid Employing Mass Drivers
Manager and Analyst Meet Again	p. 157
Gists and Schizophrenia
Appendices
Computational Request Disappointments; Results of the USC Allowability Project	p. 163
Graph Theory Overview	p. 171
The Logic of "IF" and "IF and Only IF"	p. 175
Vector Spaces Applied to Graph Theory	p. 177
References	p. 181
Index	p. 183
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